Recent content by rillchritty

@batboio Yeah there is a theorem about that: the sum and the product of two analytic functions are also analytic in that interval. If "a" and "b" are fixed, then it's quite easy to prove that f(x)+g(x)=h(x) is also in G; but the problem lies in the fact that the pair (a,b) may be different for...

I totally understand what a linear vector space is. I was able to prove that scalar multiplication of a function f(x) in G is an element of G; in other words c*f(x) is in G for all real c. That was almost trivial. I got stuck while trying to prove that the sum of two functions f(x) and g(x) in G...

Let G be the set of all real functions f(x) each of which is analytic in the interval [0,1] and satisfies the conditions: f(0)+a*f'(0)=0; f(1)+b*f'(1)=0, where (a,b) is a pair of real numbers from the set D={(a,b) in R^2: 1+b-a!=0 (is not equal to zero)}. Prove that the set G is a linear vector...